Calculating Present Values
Present value (or discounted value) is the current value of an asset (or stream of assets) that will be received in the future. You can calculate the present value of a lump sum to be received in the future or the present value of a series of payments to be received in the future.
Present Value of a Lump Sum The present value of a lump sum is the current worth of an asset to be received in the future. Alternatively, it can be thought of as the amount you would need to set aside today at a given rate of interrule
Present value (or discounted value) is the current value of an asset (or stream of assets) that will be received in the future. You can calculate the present value of a lump sum to be received in the future or the present value of a series of payments to be received in the future.
Present Value of a Lump Sum The present value of a lump sum is the current worth of an asset to be received in the future. Alternatively, it can be thought of as the amount you would need to set aside today at a given rate of interrule
est for a given time period so as to have some desired amount in the future. Suppose you want to have $20,000 for the down payment on a new home in ten years. What would you need to set aside today to reach this goal if you could invest your money and receive a 7 percent return? Using Appendix Table A.2 you could look across the interest rate rows to 7 percent and then down to ten years to obtain the factor of 0.5083. Multiplying $20,000 by this factor reveals that $10,166 set aside today would allow you to reach your goal. (Note the connection here to the rule of 72: 7 percent divided into 72 is approximately 10.28, meaning that the investment would double in about 10.28 years. Indeed, $10,166 would approximately double to $20,000 in ten years.)
Present Value of an Annuity The present value of an annuity is the current worth of a stream of payments to be received in the future. Alternatively, it can be thought of as the amount you would need to set aside today at a given rate of interest for a given time period so as to receive that stream of payments. Suppose you want to have $30,000 per year for 20 years during your retirement. What amount would you need to have invested at retirement to reach this goal if you could invest yourmoney and receive a 7 percent return? Using Appendix Table A.4 you could look across the interest rate rows to 7 percent and then down to 20 years to obtain the factor of 10.5940. Multiplying $30,000 by this factor reveals that $317,820 (10.5940 $30,000) set aside at retirement would fund this stream of payments. Note the beauty of compound interest in this result. It takes only $317,820—not $600,000—to fund a $30,000 per year retirement for 20 years if you can earn 7 percent on your financial nest egg
Present Value of an Annuity The present value of an annuity is the current worth of a stream of payments to be received in the future. Alternatively, it can be thought of as the amount you would need to set aside today at a given rate of interest for a given time period so as to receive that stream of payments. Suppose you want to have $30,000 per year for 20 years during your retirement. What amount would you need to have invested at retirement to reach this goal if you could invest yourmoney and receive a 7 percent return? Using Appendix Table A.4 you could look across the interest rate rows to 7 percent and then down to 20 years to obtain the factor of 10.5940. Multiplying $30,000 by this factor reveals that $317,820 (10.5940 $30,000) set aside at retirement would fund this stream of payments. Note the beauty of compound interest in this result. It takes only $317,820—not $600,000—to fund a $30,000 per year retirement for 20 years if you can earn 7 percent on your financial nest egg
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